Prebiotic chemistry on other worlds is going to be common. Plenty of small rocky planets will have similar chemistry. It's almost a given.
Earlier generations of stars in the galaxy could well have had planets. But really, there was only hydrogen and helium to work with, so they'd all be gas giants and not small, rocky planets.
Diminutive worlds are more likely to be rocky, and lapped by oceans and atmospheres. In the vernacular of 'Star Trek,' these would be M-class planets: life-friendly oases where biology could begin and bumpy-faced Klingons might exist.
We do care about planets like the Earth because by now we understood that life as a chemical system really needs a smaller planet with water and with rocks and with a lot of complex chemistry to originate, to emerge, to survive.
Because Alpha Centauri is so close, it is our first stop outside our solar system. There's almost certain to be small, rocky planets around Alpha Centauri A and B.
Super-Earths are how we call a family of planets... up to two times larger and about ten times more massive than the Earth.
Clearly, enriching the cosmos with heavy elements takes a while. So there's inevitably an interval between the sterile aftermath of the Big Bang and a time when the cosmic chemistry set had enough ingredients to make rocky planets (and squishy biology).
The Kuiper belt region, which I call the third zone because it lies beyond the rocky terrestrial planets and beyond the giant planets, is a bizarre frontier.
Once you've got the makings of a star, gravity draws leftover gas and dust into a giant swirling disk. The dust continues to stick together, clumping into rocky asteroids, which eventually become orbiting rocky planets. And voila: a solar system!
